Rob, et al --
I eliminated one variable: it is not the system hardware. This my most recent build. It is an Asus P9X79 Deluxe, with I7-3820 and 16 gigs of memory.
I pulled a drive from another Win7, 64-bit machine, cloned it and installed it in this system. After updating all the drivers for P9, I changed its name to Win7-1, rebooted and tried RDP from the Surface RT. It connected smoothly.
So, it ain't the hardware. It is something lurking down in the bowels of my system software. Probably not surprising as this is the system I use most and mess with the most. I try new stuff on this machine, so it has a revolving door for entry and exit. It's probably something left over from one of my experiments. For that reason, I frequently clone this drive and keep a full, bootable back-up just in case the SHTF with one of my experiments.
All things considered, though, it is mostly trouble-free and it is quick -- I73820 and an Intel SSD sorta helps with that.